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visual basic print barcode label in the form S = m dX dX . in Java
in the form S = m dX dX . QR Reader In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Quick Response Code Generation In Java Using Barcode creation for Java Control to generate, create QR Code 2d barcode image in Java applications. SOLUTION Let s start by recalling that X 2 = X X . So we can rewrite the action S in the following way: S = = 1 1 2 2 d a X m a 2 m2 1 X2 d X 2 m2 2 2 X2 m m2 1 d X2 m X2 2 X2 m2 1 2 d X 2 X m X X 2 QR Code JIS X 0510 Decoder In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. Barcode Generation In Java Using Barcode drawer for Java Control to generate, create bar code image in Java applications. String Theory Demysti ed
Bar Code Recognizer In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Paint QR In Visual C#.NET Using Barcode generator for VS .NET Control to generate, create QR Code image in VS .NET applications. Now, let s use a simple algebraic trick to rewrite the rst term. Remember from complex variables that i 2 = 1. This means that m2 2 m2 2 X X = ( 1)( 1) X2 X2 = = m2 2 2 i X X2 m2 4 4 i X X2 QR Code Drawer In .NET Using Barcode generation for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications. Draw Denso QR Bar Code In .NET Using Barcode drawer for VS .NET Control to generate, create Quick Response Code image in .NET framework applications. = m 2i 4 X 2 = m i 4 X 2
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Generate GS1 128 In Java Using Barcode creator for Android Control to generate, create GS1 128 image in Android applications. Printing Barcode In None Using Barcode encoder for Office Word Control to generate, create barcode image in Word applications. This demonstrates that the two actions are equivalent.
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At this point we have reviewed some basic techniques that help us calculate the equations of motion for a free relativistic point particle. We are going to extend this work to the case of a string moving in spacetime. A point particle has no extent whatsoever, so can be described as a zerodimensional object. We have seen that its CHAPTER 2 Equations of Motion
The worldsheet of a closed string is a tube in spacetime.
motion can be described by saying that a point particle (zerodimensional) sweeps out a path or line in spacetime (one dimension) that we call the worldline. A string, unlike a point particle, has some extension in one dimension, so it s a onedimensional object. As it moves, the string (onedimensional) sweeps out a twodimensional surface in spacetime that scientists call a worldsheet. For example, imagine a closed loop of string moving through spacetime. The worldsheet in this case will be a tube, as shown in Fig. 2.1. We can summarize this in the following way: The path of a point particle is a line in spacetime. A line can be parameterized by a single parameter, which is the proper time. As a string moves through spacetime it sweeps out a twodimensional surface called a worldsheet. Since the worldsheet is twodimensional, we need two parameters, which we can generally denote by 1 and 2 . Locally the coordinates 1 and 2 can be thought of as coordinates on the worldsheet. Or, another way to look at this is to parameterize the worldsheet, we need to account for proper time and the spatial extension of the string. So, the rst parameter String Theory Demysti ed
is once again the proper time , and the second parameter, which is related to the length along the string, is denoted by : 1 = 2 = Coordinates on the worldsheet ( , ) are mapped onto spacetime by the functions (called the string coordinates) X ( , ) (2.12) So time and spatial position on the string are mapped onto the spatial coordinates in (d + 1) dimensional spacetime as {X 0 ( , ), X 1 ( , ), , X d ( , )} Now, we need to write down the action for the string which will generalize Eq. (2.8) to our new higherdimensional world, that is, to the case of the worldsheet. This is done in the following way. Recall that the action of a point particle is proportional to the length of its worldline [Eq. (2.5)]. We just noted that a string sweeps out a twodimensional worldsheet in spacetime. This tells us that if we are going to generalize the notion of the action of a point particle, we might expect that the action of a string is proportional to the surface area of the worldsheet. This is in fact the case. Anticipating that the constant of proportionality will turn out to be the string tension, we can write this action as S = T dA (2.13) where dA is a differential element of area on the worldsheet. To nd the form of dA, we start by considering a differential line element ds 2 and introduce coordinates on the worldsheet as 1 = and 2 = . Doing a little algebra we have ds 2 = dX dX = X X d d

